Problem 99

Largest Exponential

Comparing two numbers written in index form like $2^{11}$ and $3^{7}$ is not difficult, as any calculator would confirm that $2^{11} = 2048 < 3^{7} = 2187$ .

However, confirming that $632382^{518061} > 519432^{525806}$ would be much more difficult, as both numbers contain over three million digits.

Using base_exp.txt(right click and ‘Save Link/Target As…’), a $22$ K text file containing one thousand lines with a base/exponent pair on each line, determine which line number has the greatest numerical value.

NOTE: The first two lines in the file represent the numbers in the example given above.

最大的幂

比较 $2^{11}$ 和 $3^{7}$ 并不困难，因为任何计算器都能验证 $2^{11} = 2048 < 3^{7} = 2187$ 。

然而，想要验证 $632382^{518061} > 519432^{525806}$ 就会变得非常困难，因为这两个数都包含有超过三百万位数字。

在文本文件base_exp.txt中有一千行，每一行有一对底数和指数。求这其中哪一行给出的幂的数值最大。

注意：文件的前两行就是上述两个例子。